Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).

A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity . A minimax argument is used to show that the equation has a positive homoclinic solution. The proof employs the interaction between translated solutions of the corresponding homogeneous equation. What distinguishes this result from its few predecessors is that the equation has a nonhomoge...

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusi...

SUMMARY In this letter, we provide a solution to the stabilization problem of a class of Lipschitz nonlinear systems by output feedback. Via the newly proposed nonlinearity characterization function (NCF) concept, we propose an effective method in designing an output feedback controller. Under the suggested sufficient condition which is derived by using the NCF, the proposed control scheme achi...

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient ε > 0 which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlineari...

The separate package and spillover models of photosynthetic enhancement are generalized and extended to light saturation assuming hyperbolic or exponential rate versus intensity curves. The available data are more consistent with the exponential model at high light intensities. Two significant conclusions follow: (a) the decreases in enhancement observed at high light intensities are accounted ...

We consider radial decreasing solutions of the semilinear heat equation with exponential nonlinearity. provide a relatively simple proof sharp upper estimates for final blowup profile and refined space-time behavior. actually establish global, estimate, which contains those profiles as special cases.